How come this function plays even though it can only play when "ready = true", but ready is false?

You are declaring and assigning to true a new local variable, ready, every time an input begins. Later in the listening function, when you attempt to check the value of this variable, it will be true.

To fix your script, you need to declare and initialise ready outside of the listening function. You should also be using RBXScriptSignal:Connect instead of RBXScriptSignal:connect, as the latter is deprecated. Along with this, I've made some other changes to your script that account for cases where the character may not exist, etc. and improve performance to a minor degree:

local user_input_service = game:GetService("UserInputService")
local is_ready = true

user_input_service.InputBegan:Connect(function(input, is_game_processed)
    -- Check if G key wasn't pressed.
    if input.KeyCode ~= Enum.KeyCode.G then
        return
    end
    -- Check if input was game processed.
    if is_game_processed then
        return
    end
    -- Check if not ready.
    if not is_ready then
        return
    end
    -- Check if character doesn't exist.
    local character = player.Character
    if not character then
        return
    end
    -- Check if Humanoid doesn't exist.
    local humanoid = character:FindFirstChild("Humanoid")
    if not humanoid then
        return
    end
    -- Execute code.
    is_ready = false
    humanoid.WalkSpeed = humanoid.WalkSpeed + 14
    wait(3)
    humanoid.WalkSpeed = humanoid.WalkSpeed - 14
    wait(5)
    is_ready = true
end)